Traps are cards with effects that cannot be activated immediately. They are identified by their Magenta border. You Set Traps in the Spell/Trap zone, and they are sent to the Graveyard after the effect resolves.
There are currently 3 types of Traps, which can be identified by a symbol next to the Type field on the card.
Table of Contents
Setting a Trap
While Spells are activated directly from hand, they must first be Set during your Main Phase. This is the act of placing a card face-down in the appropriate zone. Traps are Set vertically, with the top side facing your opponent, in the Spell/Trap Zone.
All Traps are at least Spell Speed 2, meaning they can activated at any time in response to other effects, assuming the game state allows it. However, you cannot activate Traps the same turn they are set.
The most basic type of Traps. You activate them, starting a Chain, and after the Chain resolves, they're sent to the Graveyard.
Just like Normal Traps, these are activated, starting a Chain. Unlike Normal Traps, they stay on the field once the Chain resolves. This kind of Trap will either have a passive effect that persists while the card is on the board, or some sort of Quick-like or Trigger-like Effect.
Used in response to the activation of a Monster effect, Spell, or another Trap. These are the only Spell Speed 3 Effects in the game, thus you can only activate a Counter Trap in response to a Counter Trap.
Unofficial Term. Those are actually Effect Monster that can be discarded to activate an effect, usually in response to something your opponent did. They are NOT Traps, and they're only referred to as such by fans, not any in-game rules or cards.
Some Traps (usually Continuous) have the effect that, once activated, they are treated as a Monster, like Embodiment of Apophis or Conquistador of the Golden Land. When you activate such a card, place it face-up in an unoccupied Main Monster Zone (any position you want, unless specified) and treat it as you would a regular Monster. However, it's still a Trap (with some exceptions), so cards like Harpie's Feather Duster still affect them.
Now that you've learned about Trap Cards in Yu-Gi-Oh, why not take a look at some of our other Yu-Gi-Oh guides?